Synthesizing electrical signals with harmonic and inter-harmonic components through generalized Fourier series

An application of the Chebyshev orthogonal polynomials and of the Legendre function approximation to efficiently synthesize electrical signals with harmonic and inter-harmonic content is presented in this paper. The synthesis is efficient in terms of the accurate results achieved in a low computational cost. After exploring the generalized Fourier series, the Chebyshev and Legendre bases were selected because they present important vector properties, namely preserving orthogonality when synthesizing electrical signals with unknown harmonic distortion and easy to compute. The correlation coefficient of the polynomials and function approximations is used to compare the accuracy of the signal synthesis with respect to the Fourier theory. The synthesis of real measured and generated test signals with harmonic and inter-harmonic content validates the numerical performance and behavior of the here-proposed application.